How many tiers? Pricing in the Internet transit market

This paper deals with the problem of ISPs selling contracts to other
(customer) ISPs. Transit ISPs implement policies which price traffic
by volume or by destination with volume discount and cheaper prices
to destinations which cost them less. The paper studies destination
based tiered pricing with the idea that ISPs should unbundle traffic
and sell pricing in tiers according to destination to maximise profits.

The background section offers a useful taxonomy of current bundles
sold by transit ISPs. This arises from discussions with ISPs.

“Transit” – conventional transit pricing, sold
at a blended rate for all traffic to all destinations ($Mbpsmonth).
Blended rates have been decreasing at 30% each year historically.
(Note – conversation with authors confirms this is usually 95th percentile).

“Paid peering” – like conventional peering but one network pays
to reach the other. off-net (destinations outside its network) and on-net
(destinations within its network) may be charged at different rates.
E.g. national ISPs selling local connectivity at a discount.

“Backplane peering” – an ISP sells global transit through its background
but discounts traffic it can offload to peers at same Internet exchange.
Smaller ISPs may buy this if they cannot get settlement-free peering
at exchange.

“Regional pricing” – transit providers price different geographical
regions differently. Rare that more than one or two extra price levels
are used for regions.

Authors show that coarse bundling can lead to reduced efficiency.
Providers lose profit and customers lose service. In an example
the blended rate price which maximises profit gives both less
profit and lower surplus to consumers than two rates for two
demand curves. An example is also given with a CDN which wants
to move demand intradomain
between two PoPs. The traffic is local to the PoPs and hence
has lower cost to the network than typical traffic but is
high in volume. If charged at the blended rate the CDN is
highly incentivised to buy a direct link itself although
the ISP providing transit could have carried that traffic
and made profit while still charging the CDN less than
paying for its own link. (Figure 2).

Section 3 of the paper creates a model of ISP profit and
customer demand. Profit is modelled as
where is the demand for traffic
in flow
traffic given the price vector (over all flows),
is the price of class traffic and is the cost
of serving traffic in flow .
Demand is modelled in two ways: Firstly with “constant elasticity demand”
(CED) – where is the
valuation parameter and is
the price sensitivity. Secondly with “logit demand”,
where
is the utility of consumer using flow is elasticity and is
an average “maximum willingness to pay”. The
have a Gumbel distribution (standard
in the logit model).
The logit model then shares flows between customers with the
share for flow (the probabiltity a given customer
will use flow ) is
.
The plus one is to allow a “no travel” decision such that the
sum to one. This, again, is standard from choice theory.

Profit maximising prices for logit and CED can be derived theoretically
but in the logit case a heuristic descent algorithm must be used
to find this optimum. Bundled prices are then tested by setting
a number of pricing points and bundling flows.

ISP costs are approximated in seveal ways (as ISPs are reluctant to
share this information).

Cost as a linear function of
bandwidth used.

Transit cost changing with distance
either as a linear cost with distance or as a concave cost with
distance.

Cost as a function of destination region (assuming
metropoliton, national, international, classified approximately
as step functions based on distance).

Cost as function of destination type (related to on-net/off-net),
approximated
by making traffic to peers cost twice that of customers (traffic between
customers allows the ISP to bill twice). This is approximated with a
factor for each distance which splits traffic into customer
or peer.

Bundling is done by several strategies:

Optimal (all combinations of a given number of bundles tried)

Demand weighted (tries to give bundles equal total flow demand but
keep high demand flows in same bundle).

Cost weighted (Similar but with cost).

Profit weighted (Similar but with profit).

Cost division (bundles divided according to cost of flow).

Index division (as above but equal number of flows in each bundle).

Data sets:

EU ISP from 2009

flows from a CDN

Internet 2 data

The basic conclusion is that only a small number of tiers are required
to get near to 100% of the possible profit. Contracts with only three
or four tiers bundled on cost and demand works well. Contracts
based on discounts for local traffic (standard practice) are sub
optimal.